000696355 000__ 03795cam\a2200529Ki\4500 000696355 001__ 696355 000696355 005__ 20230306135552.0 000696355 006__ m\\\\\o\\d\\\\\\\\ 000696355 007__ cr\cnu---unuuu 000696355 008__ 131210s2014\\\\enka\\\\ob\\\\001\0\eng\d 000696355 0167_ $$a016625222$$2Uk 000696355 020__ $$a9781447154969 $$qelectronic book 000696355 020__ $$a1447154967 $$qelectronic book 000696355 020__ $$z9781447154952 000696355 0247_ $$a10.1007/978-1-4471-5496-9$$2doi 000696355 035__ $$aSP(OCoLC)ocn864875003 000696355 035__ $$aSP(OCoLC)864875003 000696355 040__ $$aGW5XE$$beng$$erda$$epn$$cGW5XE$$dGW5XE$$dYDXCP$$dUKMGB$$dCOO 000696355 0411_ $$aeng$$hfre 000696355 049__ $$aISEA 000696355 050_4 $$aQA331 000696355 08204 $$a515/.9$$223 000696355 1001_ $$aAudin, Michèle,$$eauthor. 000696355 24010 $$aThéorie de Morse et homologie de Floer.$$lEnglish 000696355 24510 $$aMorse theory and Floer homology$$h[electronic resource] /$$cMichèle Audin, Mihai, Damain ; translated by Reinie Erné. 000696355 264_1 $$aLondon :$$bSpringer,$$c2014. 000696355 300__ $$a1 online resource (xiv, 596 pages) :$$billustrations. 000696355 336__ $$atext$$btxt$$2rdacontent 000696355 337__ $$acomputer$$bc$$2rdamedia 000696355 338__ $$aonline resource$$bcr$$2rdacarrier 000696355 4901_ $$aUniversitext 000696355 504__ $$aIncludes bibliographical references and indexes. 000696355 5050_ $$aIntroduction to Part I -- Morse Functions -- Pseudo-Gradients -- The Morse Complex -- Morse Homology, Applications -- Introduction to Part II -- What You Need To Know About Symplectic Geometry -- The Arnold Conjecture and the Floer Equation -- The Maslov Index -- Linearization and Transversality -- Spaces of Trajectories -- From Floer To Morse -- Floer Homology: Invariance -- Elliptic Regularity -- Technical Lemmas -- Exercises for the Second Part -- Appendices: What You Need to Know to Read This Book. 000696355 506__ $$aAccess limited to authorized users. 000696355 520__ $$aThis book is an introduction to modern methods of symplectic topology. It is devoted to explaining the solution of an important problem originating from classical mechanics: the 'Arnold conjecture', which asserts that the number of 1-periodic trajectories of a non-degenerate Hamiltonian system is bounded below by the dimension of the homology of the underlying manifold. The first part is a thorough introduction to Morse theory, a fundamental tool of differential topology. It defines the Morse complex and the Morse homology, and develops some of their applications. Morse homology also serves a simple model for Floer homology, which is covered in the second part. Floer homology is an infinite-dimensional analogue of Morse homology. Its involvement has been crucial in the recent achievements in symplectic geometry and in particular in the proof of the Arnold conjecture. The building blocks of Floer homology are more intricate and imply the use of more sophisticated analytical methods, all of which are explained in this second part. The three appendices present a few prerequisites in differential geometry, algebraic topology and analysis. The book originated in a graduate course given at Strasbourg University, and contains a large range of figures and exercises. Morse Theory and Floer Homology will be particularly helpful for graduate and postgraduate students. 000696355 588__ $$aDescription based on print version record. 000696355 650_0 $$aMorse theory. 000696355 650_0 $$aFloer homology. 000696355 7001_ $$aDamian, Mihai,$$eauthor. 000696355 7001_ $$aErné, Reinie,$$etranslator. 000696355 7300_ $$itranslation of (work)$$aThéorie de Morse et homologie de Floer. 000696355 77608 $$iPrint version:$$aAudin, Michele.$$tMorse Theory and Floer Homology$$z1447154959$$w(OCoLC)860812538 000696355 830_0 $$aUniversitext. 000696355 85280 $$bebk$$hSpringerLink 000696355 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-1-4471-5496-9$$zOnline Access 000696355 909CO $$ooai:library.usi.edu:696355$$pGLOBAL_SET 000696355 980__ $$aEBOOK 000696355 980__ $$aBIB 000696355 982__ $$aEbook 000696355 983__ $$aOnline 000696355 994__ $$a92$$bISE